# Parallel Solution of Sparse Linear Systems Defined Over GF(p)

Dan Page, Parallel Solution of Sparse Linear Systems Defined Over GF(p). CSTR-05-003, University of Bristol. November 2004. PDF, 257 Kbytes.
## Abstract

The second stage of processing in the Number Field Sieve (NFS) and Function
Field Sieve (FFS) algorithms when applied to discrete logarithm problems
requires the solution of a large, sparse linear system defined over a finite
field. This operation, although well studied in theory, presents a practical
bottleneck that can limit the size of problem either algorithm can tackle.
In order to partially bridge this gap between theory and practise, we
investigate and develop a fast, scalable implementation of the Lanczos
algorithm over GF(p) that can solve such systems in parallel using
workstation clusters and dedicated Beowulf clusters.

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